Elastic plastic fracture behavior and effect of band ... · CERTIFICATE This is to certify that the...
75
Elastic plastic fracture behavior and effect of band-overload on fatigue crack growth rate of an HSLA steel by OM PRAKASH National Institute of Technology Rourkela, Odisha (INDIA) -769008 A thesis submitted for the degree of Master of Technology in Mechanical Engineering (Specialization: Steel Technology) May-2014
Transcript of Elastic plastic fracture behavior and effect of band ... · CERTIFICATE This is to certify that the...
Elastic plastic fracture behavior and effect
of band-overload on fatigue crack growth
rate of an HSLA steel
by
OM PRAKASH
National Institute of Technology Rourkela, Odisha
(INDIA) -769008
A thesis submitted for the degree of Master of
Technology in Mechanical Engineering (Specialization: Steel Technology)
May-2014
Elastic plastic fracture behavior and effect of band-overload
on fatigue crack growth rate of an HSLA Steel
A thesis submitted in partial fulfillment of the requirements for award of the degree of
Master of Technology in
Mechanical Engineering
(Steel Technology)
By OM PRAKASH
(Roll No. 212MM2336)
Under the supervision of
Department of Metallurgical and Materials Engineering
National Institute of Technology Rourkela- 769008
Odisha (INDIA)
Prof. B.B.Verma
Department of Metallurgical and Materials
Engineering
National Institute of Technology
Rourkela-769008
Prof. P.K. Ray
Department of Mechanical Engineering
National Institute of Technology
Rourkela - 769008
Dedicated
To
My Respected Maa-Babu ji
I
2011
Date:
Place:
Prof. B.B.Verma
Department of Metallurgical and Materials Engineering
National Institute of Technology
Rourkela-769008
National Institute of Technology, Rourkela
Odisha (INDIA) -769008
CERTIFICATE
This is to certify that the thesis entitled, “Elastic plastic fracture behavior and effect of band-
overload on fatigue crack growth rate of an HSLA steel” submitted by Mr. Om Prakash in
partial fulfillment of the requirements for the award of Master of Technology Degree in Mechanical
Engineering (specialization of Steel Technology) at National Institute of Technology, Rourkela,
Odisha (INDIA) is an authentic work carried out by him under our supervision and guidance. To
the best of our knowledge, the matter embodied in the thesis has not been submitted to any other
University/ Institute for the award of any degree or diploma.
Prof. P.K. Ray
Department of Mechanical Engineering
National Institute of Technology
Rourkela - 769008
II
Acknowledgement
When you start any work it will be surely finish, for successful completion of any work, it
requires hard work and determination in a right direction. Behind successful completion of my
work there are many people who made it possible and whose constant guidance and
encouragement crowned all the efforts with success. Therefore, I would like to take this
opportunity to express my sincere and heartfelt gratitude to all those who made this report
possible.
First of all, I am highly grateful to my supervisor, Prof. B.B.Verma, Department of
Metallurgical and materials Engineering, N.I.T Rourkela for believing in me and encouraging
me in every step, and their great support and inspiring guidance throughout the project work,
thanks for helping me to make my one of dreams comes true.
I also wish to express my deep sense of gratitude and indebtedness to Prof. P.K.Ray,
Department of Mechanical Engineering, N.I.T Rourkela, for their inspiring guidance and
valuable suggestion throughout this project work.
I would like to express my grateful thanks to Dr. S. Sivaprasad, Principle Scientist, National
Metallurgical Laboratory Jamshedpur, for their kind support, and give us time for valuable
suggestion regarding project work.
I would gratefully acknowledge to Rourkela steel plant (RSP- SAIL), for providing HSLA steel
for this study, and I also great thankful to Mr. C. Muthuswamy, Dy. General Manager (R&C
Lab.) RSP- SAIL for providing chemical analysis of material, and his positive feedback.
My sincere thanks to our entire Lab mate friends who have great support in every level of
difficulties and make them easy. It is my pleasure to acknowledge Mr. Vaneshwar kumar Sahu
for their great kindness and continuous support in my all doubts and problem. I also thank to Mr.
Shyamu Hembram (Lab Assistant, MM), Mr. D. Sudhakar and Mr. Suhan Bekal (BiSS Technical
assistant) for their constant support during my work and operational support.
Special thanks to my god (Maa-Babu ji) and family members, without their blessings and
support, I could not have reached this destination.
Last but not the least, I wish to place my deep sense of thanks to all my friends especially to Mr.
Navratan Kumar and Mr. Ajit Kumar for their cooperation and critical suggestion during my
project works and studies.
Om Prakash
(May 2014)
III
Abstract
Study of fracture toughness and fatigue crack growth behavior are important parameters of
structural materials. These parameters can be used to predict their life, service reliability and
operational safety in different conditions. The material used in this investigation is an HSLA
steel.
In the first part of this investigation elastic plastic fracture toughness (JIc and δIc) were measured,
by resistance curve method. Tests were carried out on CT specimens, using unloading
compliance technique. These tests were conducted at three different displacement rates. It is
observed that fracture toughness decrease with increasing rate of displacement.
In the next part of this investigation effect of single overload and band-overload on fatigue crack
growth of same steel were studied. These tests were conducted on CT specimens. Single overload
and band overloads were applied under mode-I condition, during constant amplitude (tension-
tension) fatigue crack growth test. It is observed that overload and band-overload applications
resulted retardation on the fatigue crack growth rate in most of the cases. It is also noticed that
maximum retardation took place on application of seven successive overload cycles.
Keywords: Fatigue crack growth rate, Stress intensity factor, Fracture toughness, Overload,
Band-overload, CT specimen, JIc and δIc, Resistance curve.
IV
CONTENTS
Certificate…………………………………………………………………...…….……………..I
Acknowledgements…………………………………………………….……...………………..II
Abstract…………………………………………………………………...…………………....III
List of figures……………………………………………………..…………………………....VI
List of tables……………………………………………………….…………………………VIII
Nomenclature…………………………………………………………………..……………....IX
1. INTRODUCTION
1.1. Background………………………………………………………………………....1
1.2. Plan of work………………………………………………………………………...3
1.3. Objective……………………………………………………………………………5
1.4. Structure of thesis…………………………………………………………………..5
2. LITERATURE REVIEW
2.1 Introduction……………………………………………………………………….…6
2.2 Fracture mechanics…………………………………………………………………..6
2.3 Classification of fracture mechanics…………………………………………………6
2.3.1 Linear elastic fracture mechanics (LEFM)……………………………….…....7
2.3.2 Elastic plastic fracture mechanics (EPFM)…………………………………….8
2.4 Fracture toughness……………………………………………………………….......8
2.5 Fracture toughness testing……………………………………………………….…..9
2.5.1 Plane strain fracture toughness (KIc)……………………………………….…..9
2.5.2 Elastic Plastic fracture toughness (JIc and CTOD)……………………….……10
2.5.2.1 J and CTOD (δ) test procedure………………………………………...10
2.6 Affecting variables of fracture toughness…………………………………………...11
2.7 Literature on the effect of displacement rate or strain rate on fracture toughness….11
2.8 Charpy impact toughness test………………………………………………………12
2.9 Fatigue and fatigue failure mechanism…………………………………………......12
2.9.1 Stages of fatigue crack growth…………………………………………………13
2.9.2 The macro mechanism of fatigue failure……………………………………...14
2.10 Types of fatigue……………………………………………………………….….15
2.11 Fatigue crack growth………………………………………………………….….16
2.12 Different regions of crack growth rate curve………………………………….….16
2.13 Literature on effects of overload and band overload on fatigue crack growth.......17
3. MATERIAL, EXPERIMENT AND ANALYSIS DETAILS
3.1 Introduction……………………………………………….......................................21
3.2 Material…………………………………………………………………………….21
3.2.1 Chemical analysis.............................................................................................21
V
3.3 Metallography
3.3.1. Metallographic specimen preparation ……………………………………...22
3.3.2 Metallographic examination ………………………………………………...22
3.4 Hardness evaluation ………………………………………………………………..22
3.5 Tensile testing…………………………………………………………………........22
3.6 Charpy impact toughness test…………………………………………………..23
3.7 Elastic plastic fracture toughness test
3.7.1 Specimen preparation ………………………………………………………..24
3.7.2 J-Integral test ………………………………………………………………...25
3.7.3 J-analysis detail for the resistance curve test method according to
ASTM E1820-13……………………………………………………………28
3.7.4 Analysis of CTOD by δ-R Curve test method……………………………….34
3.8 Fractography of JIc tested fracture surface….………………..……………………35
3.9 Fatigue crack growth test
3.9.1 Test specimen geometry……………………………………………………..36
3.9.2 Test equipment………………………………………………………………37
3.9.3 Test program………………………………………………………………...37
3.9.4 Fatigue crack growth tests…………………………………………………...38
3.9.4.1 Constant amplitude load test………………………………………….38
3.10 Fractography of fatigue fracture surface...…………………………………...40
4. RESULTS AND DISCUSSIONS
4.1. Introduction………………………………………………......................................41
4.2 Microstructural analysis……………………………………………………………41
4.3 Phases and grain size analysis………………………………………………………42
4.4 EDS analysis………………………………….…………………………………….42
4.5 Basic mechanical properties analysis
4.5.1 Hardness……………………………………………………………………….43
4.5.2 Tensile properties……………………………………………………………...43
4.5.3 Charpy impact test property. ……………………………………………….....45
4.6 Elastic plastic fracture toughness (JIc and δIc)
4.6.1 J- integral fracture toughness (JIc) …………………………………………...46
4.6.2 CTOD fracture toughness (δIc)………………………………………………..49
4.7 Fractogrphy of JIc fracture surface…………………………………………………52
4.8 Constant amplitude loading interposed with mode-I overload and band overload…54
4.9 Fractogrphy of fatigue fracture surface……………………………………………56
5. CONCLUSIONS AND FUTURE WORK
5.1 Conclusion……………………………….......……………………………………..59
5.2 Suggested future work……………………………………………………………...60
6. REFERENCES…………………………………………………………………..……..61
VI
List of figures
1. Figure 1.1 Flow chart of work plan……………………………………………..……….4
2. Figure 2.1 Modes of deformation or fracture…………………………………………….7
3. Figure 2.2 Difference between LEFM, EPFM shown by stress strain diagram…….....….8
4. Figure 2.3- Major affecting variables of fracture toughness……………………………11
5. Figure 2.4 Effect of strain rate on fracture toughness…………………………………..11
6. Figure 2.5 Schematic relation between crack initiation, propagation and failure……..13
7. Figure 2.6 Stages of fatigue crack growth shown by compact tension specimen during
fatigue crack growth test………………………………………………………………..14
8. Figure.2.7 Flow chart of types of fatigue with details…………………………………15
9. Figure 2.8 Three different regions of crack growth rate curve………………………….16
10. Figure 2.9 Retardation in fatigue crack growth by overload and band overload application
during test……………………………………………………………………………....18
11. Figure 2.10 Single overload pulses on the constant amplitude fatigue load cycle…….19
12. Figure 2.11 Band overload (7consecutive tensile overload cycle) pulses on the constant
amplitude fatigue load cycle…………………………………………………………...19
13. Figure 2.12 Induced plastic volumetric expansion zone at the front of crack tip during a
tensile overload………………………………………………………………………...20
14. Figure 3.1 Typical round tensile test specimen following the ASTM standard E8-M…..23
15. Figure 3.2 Typical U- notch charpy impact test specimen……………………………..23
16. Figure 3.3 Orientation of compact tension specimens in L-T (Longitudinal- Transverse)
direction showing with rolling direction……………………………………………….24
17. Figure 3.4 Nominal dimensions of CT specimen with notch dimensions and side grooved
are provided, standard followed by ASTM- E1820-13………………………………...25
18. Figure 3.5 Close- up view of specimen with clevis grips and COD gauge during JIc test
of side grooved CT specimen……………………………………………………….....26
19. Figure 3.6 Load vs load line displacement plot of specimen ID: JIC-1 at room
temperature…………………………………………………………………………….27
20. Figure 3.7 Load vs load line displacement plot of specimen ID: JIC-3 at room
temperature…………………………………………………………………………….28
21. Figure 3.8 Elastic compliance correction for CT specimen rotation………………........30
22. Figure 3.9 Determination of initial compliance………………………………………..30
23. Figure 3.10 Cubic fit of valid data region in Ji vs ai curve……………………………....32
24. Figure 3.11 Definition of construction lines for data qualification……………….…….33
25. Figure3.12 Definition of construction lines for data qualification………..………........35
26. Figure 3.13 Compact tension (CT) specimen geometry (LT orientation) followed by
ASTM E 647-13………………………………………………………………………..36
VII
27. Figure 3.14 Overall arrangement to conduct fatigue crack growth test with specimen held
in clevis grips during test by computer controlled 100kN load capacity BiSS (UTM)….37
28. Figure 3.15 (a) experimental setup of specimen with COD gauge during test; (b)
measurement of crack length by Vernier calipers after test…………………………....40
29. Figure 4.1 Triplanar optical micrograph of as-received material, etched by 2% Nital...41
30. Figure 4.2 Area percentage of micro-constituents and inclusion content on
microstructure………………………………………………………………………….42
31. Figure 4.3 EDS analysis of material by SEM……………………………………….…42
32. Figure 4.4 Hardness values of steel in three different orientation………………………43
33. Figure 4.5 Typical engineering stress-strain curve obtained from a tensile test of an
HSLA steel at room temperature, showing with various features………………………44
34. Figure 4.6 Typical true stress-strain curve obtained from a tensile test of HSLA steel at
room temperature…………………………………………………………………...….45
35. Figure 4.7 Typical J-R curve for JIC-1 specimen at room temperature……………….46
36. Figure. 4.8 Typical J-R curve for JIC-2 Specimen at room temperature……………....47
37. Figure. 4.9 Typical J-R curve for JIC-3 Specimen at room temperature……………….47
38. Figure 4.10 JIc vs. displacement rate curve of tested specimens……………………….48
39. Figure 4.11 Typical δ-R curve of specimen ID: JIC-1 at room temperature…………….49
40. Figure 4.12 Typical δ-R curve of specimen ID: JIC-2 at room temperature ……………49
41. Figure 4.13 Typical δ-R curve of specimen ID: JIC-3 at room temperature ………….50
42. Figure 4.14 δIC vs. displacement rate curve of tested specimen………………………...51
43. Figure 4.15 Typical fracture surface and various region of CT specimen ID: JIC-1 after
fracture…………………………………………………………………………………52
44. Figure 4.16 FESEM micrographs of JIC-1 specimen are presented as: (A) FESEM
micrograph shows dimpled fracture surfaces that are typical of microvoid coalescence;
(B) High magnification of (A) showing the morphology of dimpled fracture surfaces and
microvoid coalescence; (C) High magnification factograph of the HSLA steel ductile
fracture surface…………………………………………………………………………53
45. Figure 4.17 – Superimposed curve of crack length versus number of cycles…………..54
46. Figure 4.18 – Superimposed log da/dN vs lo log ∆K curve……………………………55
47. Figure 4.19 Various region of fracture surface of fatigue crack growth specimen imposed
7 cycle overload………………………………………………………………………...55
48. Figure 4.20 FESEM micrographs of the constant amplitude load fatigue tested fracture
surface of Steel alloy at stress ratio (R) = 0.3 (a) A microscopic cracks and fine
microscopic cracks with stable crack growth; (b) In high magnification showing shallow
striations in the region of stable crack growth;………………………………………….57
49. Figure 4.21 FESEM micrographs of the constant amplitude load imposed with 7 cycle
tensile overload fatigue tested fracture surface of Steel alloy at overload ratio (Rol) = 1.25,
(1) Overall morphology of fracture surface; (2) In high magnification showing shallow
striations in the region of unstable crack growth………………………………………58
VIII
List of tables
1. Table 3.1 Chemical composition of an HSLA steel…………………………………..21
2. Table 3.2 Dimensions detail of the JIc Tested CT (compact tension) specimens…….....27
3. Tables 3.3 Experimental parameters for constant amplitude loading test………………39
4. Table 3.4 Various experimental parameters used during the test of specimens under
mode-I single and band overload……………………………………………………….39
5. Table 4.1 Tensile properties of an HSLA steel…………………………………………43
6. Table 4.2 Charpy impact test property …………………………………………………45
7. Table 4.3 Various JIC test parameter of investigate steel ………………………………48
8. Table 4.4 Qualification criteria of JQ as JIc and evaluation of KJIc…………………………48
9. Table 4.5 Various CTOD (δ) parameter of investigate steel……………………….…...50
10. Table 4.6 Qualification criteria of δQ as δIc …………………………………………......51
IX
Nomenclature
B specimen thickness (mm)
Be effective thickness for side-grooved specimens (mm)
BN net specimen Thickness (mm)
W specimen width (mm)
ao original crack size (crack length measured from center line of
pin hole of the specimen) (mm)
an notch length (mm)
af final crack length (mm)
(a/W)ol ratio of crack length to width of specimen at overload point
f cycle frequency (Hz)
fol overload cycle frequency (Hz)
ai crack length corresponding to the ‘ith’ (initial) step (mm)
aol crack length at overload (mm)
∆a crack extension (mm)
bo original (un-cracked) ligament length (mm)
b remaining ligament length (mm)
𝐾𝑚𝑎𝑥 maximum stress intensity factor in a cycle MPa m
𝐾𝑚𝑖𝑛 minimum stress intensity factor in a cycle MPa m
∆K stress intensity factor range MPa m
Kth threshold stress intensity factor MPa m
R loading ratio or stress ratio
Rol overload ratio
max maximum stress in a cycle (MPa)
min minimum stress in a cycle (MPa)
YS yield stress (MPa)
Y effective yield strength (MPa)
∆σ stress range (MPa)
E Young’s modulus of elasticity (MPa)
da/dN crack growth rate (mm/cycle)
Pmax maximum load of constant amplitude load cycle (N)
𝑃𝑚𝑎𝑥𝑜𝑙 maximum load at overload (N)
δ crack-tip opening displacement (CTOD) (mm)
N number of cycles or fatigue life (cycle)
1
Chapter-1
INTRODUCTION
1. INTRODUCTION
1.1. Background
Fatigue and fracture are common cause of service failure of engineering components and
structures.
To study about fatigue and fracture related problem is very important of any kind of machine
parts, components and engineering structure that is related to various type of loading condition
during their operation, so realistic fatigue crack growth and fatigue life prediction is one of the
most importance part in terms of economic and safety point of view.
Fracture mechanics is based on the inherent assumption that there already exists a crack in a
work-component or engineering structure. The crack may be man-made as a key- hole, a grooves,
a notch, a re-entrant corner, or a slot, etc. The crack may exist within a component due to
manufacturing defects like slag or impurities inclusion, cracks in a weld-ment or heat affected
zones due to irregular cooling and existence of foreign particles. A serious crack may be
nucleated and start growth during their service of the machine elements or structure (fatigue
caused cracks, nucleation of cracks in notches due to environmental dissolution).Fracture
mechanics is also applied to crack growth under fatigue loading condition. Initially, the
fluctuating load nucleates a crack, which then propagates slowly and finally the crack growth
rate per cycle accelerated and followed the fast fracture. Subsequently comes to the stage when
the crack-length is long enough to be considered critical for a catastrophic fracture failure.
Fracture mechanics is now applied comprehensively to important fields like thermal, nuclear
engineering, aerospace industries, space ships, rockets, piping, offshore structures, etc. Critical
components of thermal, nuclear power plants are made from very tough materials; but they have
too failed catastrophically once in a while. In addition, fracture mechanics can be used to evaluate
the suitability-for-service, or life extension, of existing structures.
The fatigue crack growth rate may be significantly affected by the application of overload cycles
[1]. In fatigue crack growth, load applied in the form of a single or band overloads may follow
either in mode I or mixed-mode (mode I and II). Mixed-mode overloads are common in case of,
2Date:
Place:
2
turbine blade and shafts, aircraft structures, railroads in pressure vessels, weld-ments etc. [2]. It
has been evidenced that a pure mode-I overload and multiple overloads leads to maximum crack
growth retardation, however in mode-II overload has least effect on fatigue crack growth
retardation [2, 3].
Most of engineering machine parts and structures are failed by fatigue and fracture causes
problem [4]. Our aim to understand how materials fail and how crack start and propagate, how
we control it and our ability to prevent such failures.
Fatigue resistance of engineering structures and components is mostly affected by the existence
of stress raisers such as key way, fastener holes, joints, notches, environmental conditions and
corrosion pits which promote as crack nucleation sites for fatigue cracking, during operation,
start cracks nucleate from these sites and continually propagate till final failure takes place when
the fatigue crack length approach a critical dimension [5]. From economical and safety point of
view a costly structure and machine component cannot be replaced from service simply on
detecting a fatigue crack during operation. Therefore, reliable valuation of fatigue crack growth
and fatigue life prediction are crucial so that the parts/structures can be well-timed serviced or
replaced.
Fracture toughness is a key parameter for evaluating critical strength of engineering structural in
the given environmental condition. CTOD and the J-Integral are two important fracture
evaluation parameters in EPFM and its applications are already well developed all over and used
in industrial and structural applications [6].
The fracture toughness test can be conducted for different-different conditions based on the
toughness parameters, KIc, JIc or CTOD. The value measured from the J-integral test is JIC
(critical value of J at crack initiation) which give a single point measured value of elastic plastic
fracture toughness [6]. A fracture toughness test measures the resistance of a material against
crack extension. These tests may produce either a unique single value of toughness or a resistance
curve, where a fracture toughness parameter such as K, J, or δ is plotted against the crack
extension. A particularly single fracture toughness value is usually adequate to explain a test that
fails by cleavage, because this fracture mechanism is typically unstable [4]
3
1.2 Plan of work
The overall work plan are divided in two parts as initial parts of work on basic material
characterisation as preliminary work and main work in which main objective and investigations
are focused. Here all the work plan can be visualized from flow chart as shown in figure 1.1.
Mechanical property evaluation at room
temperature
Preliminary work
(Basic material characterization)
Microstructural
examination
Tensile test Hardness test Charpy impact
test
4
Figure 1.1 Flow chart of work plan
Main work
Fatigue crack growth
rate test
Elastic plastic fracture
toughness (JIC ,δIC) test
Constant amplitude
loading, overloading
and band overload
Optimization of
retardation of
crack growth
Fatigue pre-crack upto
0.45≤ a/W ≥ 0.7
JIC test at different
displacement rate
Fractography study
Analysis of the effects of overload
and band overloads on fatigue crack
growth
Analysis of elastic plastic
fracture toughness (JIc ,δIc)
5
1.3 Objective
The aim of present investigation are-
To study the microstructural examination and evaluate basic mechanical properties of
supplied HSLA steel at room temperature.
To study the elastic plastic fracture toughness (JIc and δIc) of material at different
displacement rate and predicting its effects on fracture toughness of the material.
To study the effect of overload and band overloads applications on fatigue crack growth
and fatigue life.
To study the mechanism of fatigue crack growth under band overloading and elastic
plastic fracture toughness through fractogrpahy.
1.4 Structure of thesis
Present investigation is divided in to six chapters whose overall structure has been divided in to
two parts as preliminary work and main work and is diagrammatically represented by flow chart
in figure 1.1. The first two chapters 1 and 2 deals with an introduction and a brief review of
literature. Chapter 3 and 4 describes the details of materials and experimental procedure and their
results with discussion respectively. Chapter 5 deals with the concluding remarks and possible
future work. The list of references is presented at chapter 6 of the thesis.
6
Chapter 2
ITERATURE REVIEW
2.1 Introduction
In fracture mechanics mainly studied about how any structure or components get failed in
different type loading and environment condition, in present work fracture toughness mainly
concentrate about elastic plastic fracture toughness (JIc and δIc) and effect of band overload on
fatigue crack growth and fatigue life
2.2 Fracture mechanics
Fracture mechanics is the field of applied mechanics which deal about how to cracks propagation
in materials and when its goes to be critical, and its approaches to solid mechanics to analyze the
main driving force on a crack initiation and those of investigational solid mechanics to describe
the materials resistance to fracture or failure.
Notches, slots, key way hole and other structural discontinuities are often common in solid
materials, and this lead to assist the initiation of cracks. A sharp cracks and its further growth are
once in a while complex to investigate and predict, because the actual driving stresses and strains
at a crack tip are completely not known with the necessary accuracy. In fact, this is the reason
the classical failure theories, sophisticatedly simple as they are not satisfactorily useful in dealing
with notched and geometric discontinuities members. A powerful modern methodology in this
area is fracture mechanics, which was originated by A. A. Griffith in 1920 and has grown in
depth and scope extremely in recent decades. The aim of fracture mechanics to raise the
engineers, researches and scientist awareness to a quantifiable, practically more valuable
approaches in dealing with the stress concentrations and stress raiser driving parameters as they
affect service life, and operational durability.
2.3 Classification of fracture mechanics
Fracture mechanics can be broadly classified in two ways:
1. Linear elastic fracture mechanics (LEFM)
2. Elastic plastic fracture mechanics (EPFM)
L
7
2.3.1 Linear elastic fracture mechanics (LEFM)
LEFM is the oldest basic theory of fracture that deals with the sharp cracks in linearly elastic
bodies. The concepts of LEFM are only applicable to the materials that obey Hook’s law [4]. In
LEFM studies were first assumes that the material is isotropic and linearly elastic, by this
assumption, the stress-strain field near the crack tip is analyzed using the concepts of theory of
elasticity. When the driving stresses in front of the crack tip exceed the materials fracture
toughness, the crack will start to grow.
Again, LEFM is applicable only when the in-elastic deformation is very small as compared to
the size of the crack that is called small-scale yielding. If large regions of plastic deformations
established before the crack grows, EPFM must be used.
Most of formulas and mathematical relationship were derived for either plane strains or plane
stresses conditions, accompanying with the three basic modes of loadings on a crack subjected
body that is as-
Mode I - opening or tensile mode (the crack faces are pulled apart) and the displacement is
normal to the crack surface.
Mode II - sliding or in- plane shear (the crack surfaces slide over each other) and the
displacement is in the plane of the plate the separation is anti-symmetric and the
relative displacement is normal to the crack front.
Mode III - tearing or out of plane shear.
Figure 2.1 Modes of deformation or fracture.
8
2.3.2 Elastic plastic fracture mechanics (EPFM)
EPFM is the theory of ductile fracture, generally characterized by stable crack growth (plastic
deformation) the fracture process is accompanied by developing of large plastic zone at the crack
tip [4]. By idealizing elastic-plastic deformation as non-linear elastic, J.R. Rice proposed J-
integral, for regions beyond LEFM. In loading path elastic-plastic can be modeled as a non-linear
elastic but not in unloading part [7].
EPFM is recommended to analyse the relatively large plastic zones near crack tip of cracked
body. EPFM assumption that material is isotropic and following elastic-plastic nature. Based on
this assumption, the strain energy fields or opening displacement near the crack tips are analysed.
When the applied energy or opening displacement exceed the critical value, the crack will start
to grow. The term elastic-plastic is generally used in this approach, because of nonlinear-elastic
behaviour of the material. Here difference between them are clearly shown by below figure 2.2.
Figure 2.2 Difference between LEFM, EPFM shown by stress strain diagram
In case of EPFM generally use the J-Integral (JIc) or CTOD (δ). Crack tip opening displacement
(CTOD) suggested by Wells, popular in Europe, and the J-Integral proposed by J.R. Rice [7],
widely used in the United States However, most of investigator found that a distinctive
correlation between J and CTOD exists for a material. Thus, these two parameters are valid in
describing crack tip toughness for nonlinear and elastic plastic materials.
9
2.4 Fracture toughness
Fracture toughness is a property which defines as the ability to resist fracture, and measures in
terms of resistance to crack extension; it is one of the most essential properties of any material
for most of design and working applications. If a material has showing much more fracture
toughness it will mostly go through a ductile fracture. Brittle fracture is also very significant
property of materials with less fracture toughness [8].
Fracture mechanics, which mostly leads to the concept of fracture toughness, was broadly based
on the work of Griffith A. A. who, among other things, studied the manners of cracks in brittle
materials [9].
The experimental measurement and mathematical based conceptual analysis of fracture
toughness playing a very important role in application of fracture mechanics methods to
structural integrity valuation, damage tolerance design, fitness-for-service evaluation, and
residual strength analysis for different structures and engineering components as automotive,
ship, pressure vessels, and aircraft structures.
The stress intensity factor K (or its equivalent parameters – the elastic energy release rate G), the
J-integral, CTOD (δ), and the crack-tip opening angle (CTOA) are the key parameters mostly
used in fracture mechanics. The K factor was introduced in 1957 by Irwin [10] to deal about the
intensity of elastic crack-tip fields, and represents the LEFM. The J-integral was proposed in
1968 by J. Rice [7] to describe the intensity of elastic plastic crack-tip fields, and represents the
EPFM. The CTOD concept was introduced in 1963 by Wells [11] to assist as an engineering
fracture parameter, and can be equivalently used as K or J in practical applications. By most of
research and experimental results shows that the crack depth, specimen physical parameters,
crack configuration and geometry, loading condition all are have a mostly effect on the fracture
toughness analysis and investigation (K, G, J and CTOD). These effects are mentioned as
constraint effect on fracture toughness. [12]
2.5 Fracture toughness testing
2.5.1 Plane strain fracture toughness (KIc).
The linear elastic fracture toughness of a material is evaluate from the crack driving stress
intensity factor (K) at which a small thin crack in the material initiates to grow. It is represented
by KIc (critical stress intensity factor value at mode-I loading condition). The limiting value of
stress intensity factor required to initiate crack extension in plane strain condition at the zone
near the tip of a thin crack is called plain strain fracture toughness.
10
2.5.2 Elastic plastic fracture toughness (JIc and CTOD)
The J-counter integral has greatly employed for non-linear materials for their fracture
characterisation. By idealizing elastic-plastic deformation as non-linear elastic materials, J.R.
Rice [7] delivered the basis for covering important parameters of fracture mechanics approach
well beyond the validity limits of LEFM. The limiting value of the J-integral (which is a line or
surface integral used to describe the fracture toughness of a material having significant elastic-
plastic behavior before fracture) required to initiate crack extension from a pre-existing crack. A
large significant plastic zone at near the crack tip makes a material tough.
The plane strain fracture toughness (JIc) is define as the resistance to crack-extension under
conditions of plane strain in mode-I for very slow rates of loading- unloading or significant
plastic deformation. JIc is used for the evaluation of crack-extension resistance near the initiation
of stable crack extension. A typical J–R curve is a graphical plot of resistance to crack extension,
(physical crack extension) for ductile materials. A method to determine the plane strain fracture
toughness JIc near the onset of ductile crack growth was proposed initially by Clarke et al. [13].
Load line compact specimens and SENB test specimens with the ratio of crack length to width
a/W ≥ 0.5 were suggested for use in a fracture toughness test. [12]
2.5.2.1 J and CTOD (δ) test procedure
The steps are
Selection of specimen (CT, SENB or DC (T)).
Fatigue pre-cracking (Notch plus fatigue pre-crack must be a/W= 0.45 to 0.7).
JIc and δIc testing.
Data analysis.
Determination of provisional JIc or δIc.
Final check for validity.
By ASTM E 1820-13 [14] has two alternative methods for J and CTOD (δ) tests:
1. Basic procedure and
2. Resistance curve procedure
Resistance curve method are mostly popular because it is single-specimen and unloading
compliance technique for evaluation of fracture toughness of metallic materials and now a days
mostly used. The J-R and δ-R curve is a plot of δ or J versus ∆a (crack extension). Basic
procedure required multiple specimen and its conservative and complex analysis as compared to
resistance curve method. Data analysis for JIc and δIc are deals on chapter-3.
11
2.6 Affecting variables of fracture toughness
In brief the affecting variables are-
A. Metallurgical factors: microstructure, inclusions, impurities, composition, heat treatment,
thermo-mechanical processing.
B. Test conditions: specimen thickness, strain rate, temperature and working environment.
Figure 2.3 Major affecting variables of fracture toughness
2.7 Literature on the effect of displacement rate or strain rate on fracture toughness
Fracture toughness value is very significant parameters for design and control of failure of any
structures before engineer can use the fracture toughness values in design for fracture control
failure analysis or fitness for service, the critical fracture toughness value for particular loading
rate and service condition must be studied[15].
Figure 2.4 Effect of strain rate on fracture toughness
Fra
cture
toughnes
s
Strain rate (per sec)
Slow
Intermediate
Impact
έ <1 έ ≈ 102 to 103 έ ≈105
Strain Rate
Specimen Thickness
Temperature
Fracture Toughness
12
Several investigator were studied on effect of strain rate on fracture toughness and mostly they
were observed that fracture-toughness decreases significantly with increasing displacement rate
or loading rate or simply say strain rate. In general the fracture toughness of structural materials,
particularly steels increases with increasing temperature but decreases with increasing loading
rate [15].
Most of fracture toughness test were conducted at slow strain rates, because some materials are
strain rate sensitive, their fracture toughness value at faster loading rates can be quite different
from the measured in a slow fracture toughness test. Low strength structural steels shows a large
change in fracture toughness for different loading rates [15].
However little work has been done on the effect of displacement rate in non- linear elastic plastic
or fully plastic fracture mechanics or the critical J- Integral (JIc) and critical CTOD (δIc)
S. Kodma et al. [16] the study of the effect of strain rate on the J-Integral were had been
conducted on half inch thickness CT specimen made by Boron steel (SAE 10B35), at four
different cross head speed (Displacement rate) as 0.1, 1.0,10.0 and 100mm/min. By experimental
results they were found that JIc values decreases with increasing displacement rate.
2.8 Charpy Impact toughness test
The Charpy impact test is a very high strain-rate dynamic test in which a test specimen U-notched
or V-notched in the middle is used, and measured the amount of energy absorbed by a material
before fracture. This absorbed energy is a measure of the impact toughness and use as a
parameters to study temperature dependent ductile-brittle transition behaviour of materials. It is
mostly use in industry to measure impact toughness and DBTT of materials because of it is very
easy to prepare the specimen and easily conduct and also get the results quickly and cheaply.
2.9 Fatigue and fatigue failure- mechanism
Metal fatigue is define as a process which causes premature failure or unwanted damage of an
engineering parts or component subjected to repeated reversed or cyclic loading. Most of
machine parts and components subjected to repeated reversed or cyclic loading are found to fail,
when the actual maximum stress are below the actual ultimate strength of the material, and
sometimes at stress values even below the actual yield strength of materials [17]. Fatigue is
estimated to cause 80- 85% of all operational service failures of metallic components and
structures such as ships, bridges, aircraft, machine components, etc. are occurring under variable
or constant fluctuating load or cyclic stresses, failure can occur at stress significantly below than
the actual ultimate tensile or yield strengths of material under a static load condition.
13
2.9.1 Stages of fatigue crack growth
Fatigue proceeds in three different stages as:
1. Crack initiation
Region–I:
Early development of damage.
difficulty in defining crack size (dislocation, micro-crack, porosity etc.)
2. Crack propagation
Region–II- crack growth
Deepening of initial crack on shear planes.
crack can first be observed in an engineering sense.
Stage II crack growth
well-defined crack growth on a planes normal to maximum tensile stress.
crack growth can be observed.
3. Final catastrophic failure
ultimate failure of materials.
Figure 2.5 Schematic relation between crack initiation, propagation and catastrophic failure.
Crack InitiationCrack propagation
Region-I
Region-II Region-III
Final catastrophic failure
14
2.9.2 The macro mechanism of fatigue failure
The micro mechanism of fatigue failure is briefly discussed as-
1. Crack initiation - It is occur in the areas of localized stress concentration (near stress
raisers) such as key ways, notches holes, slots, also cracks may start at surface, and due
to geometrical discontinuity, and sites of inclusions and existing cracks.
Figure 2.6 Stages of fatigue crack growth shown by compact tension specimen during
fatigue crack growth test
2. Incremental crack propagation - By further increasing the stress levels and the process
continues, propagating the fatigue cracks across the grains or along the grain boundaries,
by this slowly increasing the crack size.
3. Final catastrophic failure - As the area becomes too deficient to resist the induced
stresses results as a sudden fracture in the structures or a machine components. At the
final stage of fatigue material ultimately failed.
15
2.10 Types of Fatigue
Figure 2.7 Flow chart of types of fatigue with details.
Fatigue
Fatigue of uncracked companents
No any pre-exist cracks initiation controlled
fracture.
Examples: almost any small components like
gudgeon pins, ball races, gear teeth, axles, crank
shafts, drive shafts.
Fatigue of cracked structures
By pre-exist Cracks; propagation controlled
fracture.
Examples: practically any large structure,
specially those having welds: bridges,
ships, pressure vessels, automotive parts.
High cycle fatigue
Fatigue at stresses below general yield;
≥ 104 cycles to fracture.
(σfatigue < σ yield ; Nf > 10,000)
Examples: all rotating or vibrating
systems like wheels, shaft, axles, clutch
and engine components etc.
Low cycle fatigue
Fatigue at stresses above general
yield; ≤ 104 cycles to fracture.
(σfatigue > σ yield; Nf < 10,000)
Examples: core components of
nuclear reactors, air-frames, turbine
parts and components, component
subject to occasional overloads.
16
2.11 Fatigue crack growth
The common of fatigue life may be taken up in the propagation of a crack. By the application of
fracture mechanics approaches it is likely to predict the number of cycles used up in growing a
crack to some specific length or to final fracture. The effects of load ratio on the fatigue crack
growth behavior are generally available for some standard geometric specimens [18]. Fatigue
crack growth behavior mostly depends on the state of stress near at the notch tip zone, the
geometry, and shape of the key hole, notches and loading parameters etc.
The aircraft industry mostly concerned about crack growth and proper and realistic prediction of
fatigue crack growth for safe-life or fail-safe design approach. Thus by well knowing the material
crack growth behavior and characteristics with regular examinations, a cracked structures or
machine component may be kept in operational service for an extended valuable life [17].
2.12 Different regions of crack growth rate curve
Theoretical and investigational linear elastic methodologies tries to define the stable and unstable
crack growth by a fatigue crack growth which can be defined as incremental crack growth (da)
divided by increment in number of cycles (dN). This fatigue crack growth rate (da/ dN) and stress
intensity factor range can be inter-related by Paris law as da/ dN = C(ΔK)m ( where m and C are
material constants and ΔK= Kmax - Kmin. If a graph is plotted between log (da/ dN) versus log
(ΔK) it will be follow the trends, that is shown in figure 2.8. This graph can be divided in to three
regions. The most common way to represent fatigue crack growth rate data is a plot between log
da/dN versus log ΔK.
Figure 2.8 Three different regions of crack growth rate curve.
17
Region-I: This region is described as crack initiation zone in which increase in log da/dN
asymptotically with log (ΔK). It is the fatigue threshold zone where the ΔK is value is not enough
to propagate a crack. Crack cannot be initiated until and unless ΔK reaches certain threshold
value known as ΔKth. Below this the growth in da/dN is too low that cannot be measured
experimentally. This regions is normally contributed by crack nucleation and early growth
initiation state. Above threshold da/dN will increase in a steep manner.
Region II: It is also called as crack propagation or Paris regime in which crack growth rate is
followed a linear variation with respect to increasing in log ΔK. This region is characterized by
stable crack growth.
Region III: This zone is described by fast fatigue crack growth rates. Since the material is
approaching the point of unstable fracture, and the Kmax) of the cycle reaches to critical fracture
toughness (KC) of materials.
2.13 Literature on effects of overload and band-overload on fatigue crack growth:
An overload is a pulse or a set of pulses of higher amplitude on a constant amplitude fatigue
loading as shown in figure 2.10 and 2.11 the crack propagation rate retards considerably after
the overload pulse [19, 20]. During region- II of fatigue crack growth, overloads can have a very
significantly effect on fatigue life. During the overload the very high crack tip strain induces a
large zone of plastic deformation ahead of the crack. During unloading elastic material tries to
regain its original state, however the plastic zone cannot regain the original state and, therefore,
compressive residual stresses are developed in the locality of the crack tip.
By application of overload and band overload on fatigue cycle results in a plastic volumetric
expansion that acts to close the crack. Any subsequent cycles have, first of all, to rise above the
cracks pre-compression before causing damage. Therefore the crack growth rate is retarded. This
is demonstrated in Figure 2.12, this phenomena is well-known as crack retardation. This
influence retards the fatigue crack growth rate until it has not to successfully propagate through
the affected zone, after that it continues in general.
Several investigators [21-28] observed that changes in magnitude of cyclic load may result in
retardation or acceleration in fatigue crack growth rate. Extensive published data show that the
rate of fatigue crack growth rate under constant amplitude cyclic load fluctuation can be retarded
significantly as a result of application of single or multiple tensile overload cycle having peak
load greater than that of the constant amplitude loading cycles. Von Euw [29] observed that the
minimum value of fatigue crack growth rate did not occur immediately after the high tensile load
cycle but that the rate of growth retardate to a minimum value. This retardation region has been
termed as delayed retardation, shown on Figure 2.9 Several models have been proposed to
explain the phenomenon of crack growth delay. In general, these models attribute the delayed
behavior to crack-tip blunting, residual stresses [30, 31] crack closure [32], or a combination of
18
these mechanisms. A crack tip blunting model advocates that high tensile load cycles cause crack
tip blunting, which in turn causes retardation in fatigue crack growth at the lower cyclic load
fluctuations until the crack is re-sharpened. The residual stress model suggest that the application
of a high overload cycle generate residual compressive stresses in the locality of the crack tip
that reduce the rate of fatigue crack growth rate. Finally, the crack closure model postulates that
the delay in fatigue crack growth is caused by the formation of a zone of residual tensile
deformation left in the wake of a propagating crack that causes the crack to remain closed during
a portion of the applied tensile load cycle. Consequently, fatigue crack growth delay occurs
because only the portion of the overload cycles above the crack opening level is effective in
extending the crack.
Figure 2.9 Retardation in fatigue crack growth by overload and band overload application
during test.
Fatigue crack growth delay has been shown to be strongly dependent on all the loading variables,
such as the stress intensity factor fluctuation, of the high tensile load cycle, the ∆K for the
constant amplitude cycles (Fig. 9.20) [33], the stress ratios of these ∆K values and the number
of constant amplitude cycles between the high tensile load cycles [33-36]. Extensive research is
necessary to further our understanding of the significance of these variables in order to develop
equations that can be used to predict accurately the fatigue life of components subjected to single
or multiple high tensile load cycles.
19
Figure 2.10 Single overload pulses on the constant amplitude fatigue load cycle.
Figure. 2.11 Band overload (7 consecutive tensile overload cycle) pulses on the constant
amplitude fatigue load cycle.
Δσ
No. of cycle (N)
σmax
σmin
Overload pulseRetarded
Δσ
No. of cycle (N)
band overload (7 overload cycle )
20
Figure 2.12 Induced plastic volumetric expansion zone at the front of crack tip during a tensile
overload [4]
21
Chapter 3
ATERIAL, EXPERIMENT AND ANALYSIS DETAILS
MATERIAL, EXPERIMENT AND ANALYSIS DETAILS
3.1 Introduction
The Elastic plastic fracture toughness test (JIc and CTOD) at different displacement rate, and
fatigue crack growth rate tests under different loading conditions on an HSLA steel. All tests
were done using a 100kN, servo-hydraulic universal testing machine. Tests were on compact
tension (CT) specimens under displacement control for elastic plastic fracture toughness test.
The fatigue crack growth tests were done on CT-specimens under load control condition and
also followed overload and different successive number of overloads (band overload) cycles on
the specimens during test.
3.2. Material
The material studied in current investigation is an HSLA steel, collected from Rourkela steel
plant, Rourkela. The chemical composition of material is provided in Table 3.1. This alloy has
good weldability and suitable for automobile and piping industries.
Table 3.1 Chemical composition of the HSLA steel as:
Material
(% wt.) C Mn Si P S Al V Nb Mo Fe
0.2 1.27 0.25 0.021 0.014 0.05 0.001 0.005 0.001 balance
M
22
3.3 Metallography
3.3.1. Metallographic Specimen Preparation
For metallographic examination purpose small piece of approximately 12mm x 12mm x 10mm
size were cut with the help of a hacksaw from the as-received material. The sample so cut is
grinded by wheel, belt grinders and various grades of silicon carbide abrasive papers (emery
papers). The specimen subsequently polished on sylvet cloth using diamond paste of particle
sizes of 1μm~ 0.25μm. The metallographic specimen subsequently etched with freshly prepared
2% Nital solution.
3.3.2 Metallographic Examination
To examine the microstructure of as-received material, well etched metallographic specimens of
the material were prepared in three directions: L-T, L-S, and T-S. Then they were examined in
all three directions with the help of an optical microscope (Carl Zeiss Microscopy).
3.4 Hardness Evaluation
Hardness were examine in three directions L-T, L-S, and T-S surfaces with the help of a Vickers
Hardness using a load of 5 kgf.
3.5 Tensile Testing
Tensile tests are performed on round bar specimens of diameter 6 mm and gauge length 30 mm
out of the as received material. The tests were conducted following the ASTM standard E8-M
[37]. The nominal dimensions of the tensile specimens are shown in Figure 3.1.
All tests were carried out with the help of a 100kN servo-hydraulic Universal Testing Machine
connected with computer that is running Windows based monotonic application software
supplied by BiSS. The software has facility for controlling the test control parameters, like strain
rate, cross head speed and data acquisition system on load, displacement and extensometer in
the channels. During test using a 25 mm gauge length extensometer at room temperature, carried
out at a displacement rate 1 mm/min. The true strain was measured through 25mm gauge length
extensometer, mounted to the mid-section of the specimen length.The tensile test generated data
after test were investigated to estimate the various mechanical properties of the material.
23
All Dimension in mm
Figure 3.1 Typical round tensile test specimen following the ASTM standard E8-M [37].
3.6 Charpy Impact Toughness test
Charpy impact toughness test were conducted on Indian standard specimen with dimension
10mmX10mm square cross section with 55mm length, provided 5 mm deep U-notch notched at
one side at mid-point of its length. [38]
Figure 3.2 Typical U- notch charpy impact test specimen [38].
Charpy impact energy and impact toughness are determined by the following relationship as:
Impact strength = Energy absorbed (kJ)
Cross−sectional area at the breaking point (m2)
24
3.7 Elastic plastic fracture toughness test
3.7.1 Specimen Preparation
The Elastic plastic fracture toughness tests in this research were conducted on CT specimens in
L-T (Longitudinal- Transverse) orientation, shown in figure 3.3. Considering the available form
of the material, standard 1-CT specimens with reduced thickness were machined following the
guidelines of ASTM E 1820-13 [14], is shown in Figure 3.4, the specimens were fabricated such
that the notch direction is transverse direction and loading direction in longitudinal direction in
the L-T orientation with respect to the plate dimension. Typical configuration of a specimen is
shown in Figure 3.4. The designed dimensions of the specimens were; thickness (B) ~12mm,
width (W) is ~ 51mm and machine notch length (an)~9.5mm. For proper plane strain deformation
and straight crack growth along the crack front, side grooves were provide with each side. The
side grooving was carried out by keeping a notch angle 60 degree of to a depth of approximately
1.2 mm on each side of the specimen. This was done to enhance the stress tri-axialty at the crack
tip and net thickness of specimen are around 9.4mm.The dimensions of the specimens used in
this investigation are shown in Table 3.2.
Figure 3.3 Orientation of compact tension specimens in L-T (Longitudinal- Transverse)
direction showing with rolling direction.
25
All dimensions in mm
Figure 3.4 Nominal dimensions of 1-CT specimen with notch dimensions and side grooved are
provided, standard followed by ASTM- E1820-13[14].
3.7.2 J-Integral test
The fracture toughness tests in this investigation were done on 1-CT (compact tension) with
reduced thickness specimens. JIc test had been done in two processing test steps as first on is
fatigue pre crack up to a/W is 0.45 to 0.70 by ASTM-E1820-13 [14]. And second one is JIc test
of pre cracked specimen, by machine each specimen were pre cracked by fatigue, to produce a
very sharp initial crack. Only three typical crack length to width ratios (a/W) (0.45, 0.58 and
0.542) are selected and analysed in this investigation. All the pre-cracking experiments were
done by computer controlled 100 kN load capacity BiSS servo-hydraulic universal testing
machine using application software VAFCP (variable amplitude crack propagation) fatigue
software. The software permitted on-line monitoring of the crack length (a), compliance, ΔK,
load range and da/dN etc. All fatigue pre-cracking were done at a stress ratio of (R) 0.3 using a
frequency of 10Hz and with a constant ΔK is 15 MPa√m. All load line knife edge CT specimens
were pre-cracked to achieve a total crack length of approximately 26 mm, which corresponds to
≈ 0.45-0.6. The total crack lengths (including starter notch configuration plus fatigue pre-crack)
for each specimen are given in Table 3.2. The crack length during test were measured by machine
26
using compliance technique with the help of COD gauge connected through the specimen during
test.
Monotonic J-integral tests were carried out, as per the requirements of ASTM standard E1820-
13 [14] on a computer controlled 100kN capacity BiSS servo-hydraulic universal testing machine
using J-R Test-2370 based application software using a different displacement rate at room
temperature were loading displacement was controlled. Specimens of desired crack length were
loaded to the desired displacement and then unloaded it, this loading and unloading process had
done up to certain termination condition followed by ASTM E 1820-13 [14]. Unloading rate
were kept sufficiently slow as compared to loading rate for maintain significant linear unloading
line. J value is calculated at several points along an unloading curve. All tests were conducted
under monotonic loading conditions using of single specimen unloading compliance technique
as a reference method. In this method the crack lengths are determined from elastic unloading
compliance measurements. This is done by carrying out a series of sequential unloading and
reloading during the test, the interruptions being made in a manner that these are almost equally
spaced along the load versus displacement record. These experiments have been carried out
following the ASTM E 1820-13 [14] standard. In the single specimen J-integral tests unloading
should not exceed more than 50% of the current load value or 20% of Pm (maximum pre-crack
load).
Figure 3.5 Close- up view of specimen with clevis grips and COD gauge during JIC test of side
grooved 1-CT specimen.
27
Table 3.2 Dimensions detail of the JIc Tested CT (compact tension) specimens.
Specimen ID
Specimen dimensions
in mm
W B BN Be an a
JIC-1 50.8 11.5 9.3 11.08 9.70 22.86
JIC-2 51 11.95 9.35 11.38 9.60 29.63
JIC-3 51 11.9 9.4 11.37 9.60 27.64
Figure 3.6 Load vs Load line displacement plot of specimen ID: JIC-1 at room temperature.
0
5
10
15
20
25
30
35
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6
Specimen ID : JIC-1
Pre-cracked a/W : 0.450
Load Line Displacement
Load
(kN
)
28
Figure 3.7 Load vs Load line Displacement plot of specimen ID: JIC-3 at room temperature.
3.7.3 J-integral analysis detail for the Resistance curve test method according to ASTM
E1820-13 [14]
Calculation of J-integral For the compact tension (CT) specimen at a point corresponding
incremental crack length (a (i)), incremental displacement (v(i)), and incremental load (P(i)) on
the specimen load versus LLD plot calculate as:
( ) ( )i el i pl iJ J J
The magnitude of Ji is the sum of its elastic and plastic component denoted by Jel(i) and Jpl(i).
The elastic component of Jel(i) was calculated using the equation 2 2
( )
(1 )iel i
K vJ
E
And calculation of K(i) —For a load P(i) , corresponding K(i) as:
( )
( ) 0.5( )
i ii
N
P aK f
BB W W
Where K(i) is the elastic stress intensity parameter.
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5 3
Partial unloading
Load Line Displacement (LLD) in mm
Load
(kN
)
1
𝑐
Specimen ID : JIC-3
Pre-cracked a/W = 0.542
29
For calculation of iaf
W
as:
2 3 4
1.5
2.0 0.886 4.640 13.320 14.720 5.60
1
i i i i i
i
i
a a a a a
W W W W Waf
W a
W
Calculation of Crack Size (ai)—From J-R curve analysis using unloading compliance
technique, the crack size is calculate as:
2 3 4 5
( ) ( ) ( ) ( ) ( )1.000196 4.06319u 11.242u – 106.043u 464.335u 650.677uii i i i i
a
W
Where
( ) 0.5
( )
1
1i
e c i
uB EC
And ( )c iC , the crack size valuation may be modified for rotation.
Compliance is corrected as:
( ) *
sin cos sin cos
ic i
i i i i
CC
H D
R R
where (Figure 3.8):
Ci = measured elastic compliance of specimen (at the load line),
H* = initial half-span of the load points (centre of the pin holes),
R = radius of rotation of the crack centreline,
2
W a where a is the updated crack size,
D = half of the initial distance between the displacement measurement points,
θ = angle of rotation of a rigid body element about the unbroken mid-section line, or
md = total measured load-line displacement.
30
Figure 3.8 Elastic compliance correction for CT specimen rotation
And,
1 1
2 2
2sin tan
m
i
dD
D
RD R
The slope of each unloading line was calculated by linear regression analysis. The inverse of
the slope is the compliance (Ci) of the specimen corresponding to the load from which the
unloading has been carried out.
Figure 3.9 Determination of Initial Compliance.
31
The plastic component of Jpl(i) were calculated using the following equation as-
1 ( 1) ( ) ( 1) ( 1)
( ) ( 1) ( 1)
( 1) ( 1)
( )( )1
2
pl i i i pl i pl i i i
pl i pl i i
i N i
P P V V a aJ J
b B b
Where-
1
( ) 2.0 0.5220i
pl i
b
W
and
( 1)
( 1) 1.00 0.760i
i
b
W
Where-
( )pl iV = plastic portion of the LLD, and
( ) ( )pl i i i LL iV V PC
and
( )LL iC = experimental compliance, i
V
P
corresponding to the current crack size, ia .
An experimental elastic compliance, ( )LL iC , calculated from the following equation:
2 2 3 4 5
( )
12.1630 12.219 20.065 0.9925 20.609 9.9314i i i i i i
LL i
e i
W a a a a a aC
EB W a W W W W W
Where-
2
N
e
B BB B
B
32
Plotting procedure of J-R Curve:
The J-integral values (Ji) and the equivalent crack length (ai) values were plotted as shown in
figure 3.10, and cubic fit of valid data region for finding intercept value of the fitted curve and
this is the value of aoq. If an elastic unloading compliance technique is used, modification the J-
R curve according to the process for each ia value, calculate a corresponding ia as follows:
i i oqa a a
Figure 3.10 Cubic fit of valid data region in Ji vs ai curve
Plot Ji versus Δai as shown in Figure 3.11. Draw a construction line according to the following
equation:
J 2 aY
According to above equation draw the construction line, after that plot an 0.15 mm exclusion
line parallel to the construction line intersecting the abscissa at 0.15 mm. Plot a second 1.5mm
exclusion line parallel to the construction line intersecting the abscissa at 1.5 mm. Plot all
J a data points that fall inside the area enclosed by these two parallel lines and covered by
limit value of J and that shows as-
olimit
bJ
7.5
Y
Plot a 0.2mm offset line parallel to the construction and exclusion lines intersecting the
abscissa at 0.2 mm.
Using the least squares method for determining a power regression line of the following
form:
33
1 2
aln ln ln lnJ C C
k
The load vs. load line displacement (LLD) data obtained from the tests were analysed to compute
the magnitude of crack extension (Δai) and the corresponding Ji integral value at each unloading
sequence as shown in fig. 3.11.
Figure 3.11 Definition of construction lines for data qualification
Qualification of JQ as JIc
a size independent value of fracture toughness Q IcJ J , if:
Thickness and Initial ligament fulfil the validity criteria
0
10,
Q
Y
JB b
Evaluation of JIcK as:
2(1 )
IcJIc
EJK
34
3.7.4 Analysis of CTOD by δ-R curve test method—
Form this method, calculations of CTOD for any point on the force-displacement curve are
calculate from the relation as shown below:
i
Y
J
m
And where 2 3
0 1 2 3YS YS YS
TS TS TS
m A A A A
With: A0=3.62, A1 = 4.21, A2=4.33, and A3=2.00. For calculation of δi requires 0.5YS
TS
.
The maximum δcapacity for a specimen is given asfollows:
0max
10
b
m
Construction of δ-R curve
The δi values and the corresponding crack extension ∆ai values were plotted as δ-R curve. The
procedure for construction of δ-R Curve is same as J-R curve. Some value is different from J-R
curve during construction of δ-R Curve as:
Firstly plot Plot δi versus Δai , Draw a construction line by using the following equation:
δi = 1.4 Δai
for δlimit is calculate as:
δlimit = bo / 7.5m,
35
Figure 3.12Definition of Construction Lines for Data Qualification
Qualification of δq as δIc : a size-independent value of fracture toughness, δQ = δIc, if:
The initial ligament, 10o Qb m
3.8 Fractography of JIc tested fracture surface
Approximately 12 mm long parts of samples were cut from the fractured surface of tested
specimen for fractographic examinations. The specimen parts were selected as the parts having
contained as fatigue pre-cracked and the fractured surface. The fractured surfaces were well
cleaned by ethenol and were examined with the help of a field emission scanning electron
microscopy (FESEM). The various images taken by FESEM at different magnitude and
resolution for proper understanding the fracture behaviour of the material.
36
3.9 Fatigue Crack Growth Test
3.9.1 Test Specimen geometry
Fatigue crack growth tests, were conducted on CT (Compact Tension) specimens with a narrow
notch and reduced thickness, which is fabricated from 12 mm thick plate. The CT specimens
were made in the L-T orientation, both sides of the specimen surfaces were given mirror-polish
with the help of different grades of emery papers with the loading aligned in the longitudinal
direction and notch given in the transverse direction, standard ASTM E647-13 [39] are followed
for specimen geometry design. The dimensional details of specimen are presented in Figure 3.13.
All dimensions in mm
Figure 3.13 Compact tension (CT) Specimen geometry (LT orientation) followed by ASTM E
647-13 [39]
37
3.9.2 Test equipment
The machine used for the fatigue crack growth tests was a computer controlled BiSS servo-
hydraulic universal testing machine having 100 kN load capacity using VAFCP (variable
amplitude crack propagation) fatigue application software.
Figure 3.14 Overall arrangement to conduct fatigue crack growth test with specimen held in
clevis grips during test by computer controlled 100kN load capacity BiSS Universal test
machine (UTM).
3.9.3 Test program
Computer controlled 100kN load capacity BiSS Universal test machine (UTM) using VAFCP
(variable amplitude crack propagation) fatigue software.The software permitted on-line
monitoring of the crack length (a), compliance, ΔK, load range and the crack growth rate per
cycle, (da/dN). All test were conducted at constant load mode at stress ratio of (R) 0.3 and using
10Hz frequency. For fatigue crack growth test were perform on CT specimens in accordance
with ASTM E647-13 [39]. This test program runs under a room temperature. The VAFCP
application software are used program has the ability to use the compliance method to measure
crack length with the help of a COD gauge.
38
3.9.4 Fatigue crack growth tests
The specimen surfaces were stick by graph paper for manually examine the crack extension
during the test as well. The COD gauge was mounted on the knife edges of specimen to monitor
crack extension by software based program. Fatigue pre-cracking was done under mode-I
loading (crack opening mode) at constant amplitude loading mode to an a/W ratio of 0.24.
Following three different case of crack growth tests were performed in this investigation:
(i) Constant amplitude loading with constant stress ratio (R).
(ii) Constant amplitude loading with single overload in mode-I.
(iii) Constant amplitude loading with band (multiple) overload in mode-I.
When the tests were conducted in constant load control mode (i.e. increasing ∆K with crack
extension), using a Computer controlled BiSS 100kN load capacity servo-hydraulic dynamic
universal testing machine (UTM) (shown in figure 3.12). All the three sets of tests were done in
ambient temperature condition at a frequency of 10 Hz and load ratio (R) of 0.3.
For determining of the stress intensity factor range (∆K) [39] for CT specimen were calculated
by following equation:
2 3 4
1.5
20.886 4.64 13.32 14.72 5.6
1
PK
B W
Where 𝛼 = 𝑎
𝑊 ; expression valid for
𝑎
𝑊≥ 0.2
3.9.4.1 Constant amplitude load test
In case-(i) - CT specimens were tested under constant amplitude load mode maintaining a fixed
load ratio, R = 0.3.
In case- (ii) - CT specimens were tested under same loading conditions with single tensile
overload are applied in mode-I at, 𝑎
𝑊= 0.28, with overload ratio ( Rol) were applied 1.25, in 1
Hz frequency.
The overload ratio is 𝑅𝑜𝑙 =𝐾𝑜𝑙
𝐾𝑚𝑎𝑥𝐵
Where, Kol is over load stress intensity factor, and 𝐾𝑚𝑎𝑥𝐵 is the maximum stress intensity factor
for base line test. The specimens were subsequently subjected to mode-I constant amplitude load
cycles after overload.
39
In case- (iii) constant amplitude loading with band (multiple) tensile overload were applied in
mode-I, approximately same size and dimensions, CT specimens were tested in order to
investigate the effect of a band overload in mode-I
After band overload on the subsequent constant amplitude fatigue crack growth test were
allowed for continue the test. The crack was allowed to grow up to , 𝑎
𝑊= 0.67. Band-overload
tests ware followed by multiple tensile overload at 𝑎
𝑊= 0.28, and overload ratio ( Rol) were
applied 1.25, in 1 Hz frequency. The number of band overload were applied during test are 3,
5,7,10,100, in the same crack opening mode.
The experimental parameters for all the tests are mentioned in Tables 3.3 and 3.4 respectively.
Tables 3.3 experimental parameters for constant amplitude loading test.
Pmax
(kN)
Pmin
(kN ) R
ao
(mm)
af
(mm)
f
(Hz)
11.8 3.54 0.3 11 34.34 10
Table 3.4 various experimental parameter that were used during the test of specimens under
mode-I single and band overload
Pmax
(kN)
Pmin
(kN )
𝑃𝑚𝑎𝑥𝑜𝑙
(kN) R Rol (
𝑎
𝑊)𝑜𝑙
ao
(mm)
aol
(mm)
af
(mm)
fol
(Hz)
f
(Hz)
11.8 3.54 14.75 0.3 1.25 0.28 11 14.154 34.00 1 10
40
Figure 3.15 (A.) experimental setup of specimen with COD gauge during test;
(B.) Measurement of crack length by Vernier calipers after test.
3.10 Fractography of fatigue fracture surface
Approximately 12 mm long parts of samples were cut from the fractured surface of fatigue crack
growth tested specimen for fractographic examinations. The specimen parts were selected as the
parts containing as fatigue crack propagated parts for constant amplitude loading specimen and
for 7 cycle Overloading specimen containing as the zone as before and after overloading portion
with overloading zone The fractured surfaces were well cleaned by ethanol and were examined
with the help of a field emission scanning electron microscopy (FESEM). The various images
taken by FESEM at different magnitude and resolution for proper understanding the fracture
behaviour of the material.
A.
..a
B.
41
Chapter 4
R ESULTS AND DISCUSSIONS
4.1 Introduction
The characterisation of microstructural feature, phase and mean grain size analysis, is described
in section 4.2 to 4.4. Basic mechanical properties of as-received material are discussed in section
4.5.Fracture toughness test related results and tested fracture surface fractography are discussed
in section 4.6 and 4.7 respectively. Fatigue crack growth rate test results and tested fracture
surfaces fractography deals on section 4.8 and 4.9 respectively.
4.2 Microstructural analysis
Well-polished and etched metallographic specimens were studied using an optical microscope
(Carl Zeiss Microscopy). Typical optical micrographs of as-received material are illustrated in
Figure 4.1. The white portion of microstructure refers to ferrite and light black portion refers to
pearlite. The dark black portion appears as martensite along with carbide precipitate throughout
structure in this steel. The ferrite matrix gives ductility and toughness to the investigated
steel.This optical microstructure illustrates the alignment and grain structures of the rolled plate
in three mutually orthogonal directions. The microstructures of all three directions were
superimposed to obtain the 3-D view and shown in Figure 4.1.
Figure 4.1 Triplanar optical micrograph of as-received material, etched by 2% Nital.
42
4.3 Phases and grain size analysis
Phase analysis of as-received material were investigated by Carl Zeiss Microscopy and is shown
in Figure 4.2. The alloy contents 62 % ferrite, 31% pearlite and 7% martensite along with carbide
precipitates. However identification of martensite and carbide precipitates need TEM analysis.
Mean grain size distribution is found as 15.417µ by taking average of three consecutive reading
from Microscopy using ASTM E 1382 for grain size analysis.
Figure 4.2 Area percentage of micro-constituents and inclusion content on microstructure
4.4 EDS analysis
To determine the elements present in as-received material, EDS analysis is done. EDS spectrum
of investigated samples are shown in Fig.4.3.
From that figure it was observed that in the steel contents large amount of Mn and micro-alloying
elements, Mo, Nb and V.
Figure 4.3 EDS analysis of material by SEM.
ferrite62%
pearlite31%
martensite+inclusion7%
Area percentage of micro-constituents and inclusion
content
ferrite pearlite martensite+inclusion
43
4.5 Basic mechanical properties analysis
4.5.1 Hardness
Hardness values were measured in all three perpendicular directions e.g., L-T, L-S and T-S
surfaces with the help of a Vickers Hardness Testing machine applying a load of 5 kgf. For each
surface five indentations were taken to get mean value of hardness of the steel.
The hardness data in all three directions are shown in Figure 4.4.
Figure 4.4 Hardness values of steel in three different orientation
4.5.2 Tensile properties
The tensile tests were conducted and the engineering stress-strain plot and true stress-strain plot
are shown in Figure 4.5 and 4.6 and the tensile properties in Table 1. The tensile values are taken
by the average of two test. The 0.2% yield stress and ultimate tensile stress values from the two
tests are showed almost same.
Table 4.1 Tensile properties of HSLA steel
Material
σYS
(MPa)
Yield
Load
(kN)
σUTS
(MPa)
Peak
Load
(kN)
E
(GPa)
Poission
ratio
(υ)
Strain
Hardening
exponent
(n)
Strain
Hardening
Co-efficient
(K)
(MPa)
%
Elongation
in 25mm
gauge
length
%
Reduction
in Area
HSLA
steel 622.45 17.69 778.62 22.22 210 0.33 0.156 1439.65 27 47.9
50
80
110
140
170
200
L-T T-S L-S
Average hardness value in three different orientation
of specimen
166HV5 163HV5186HV5
44
Figure 4.5 Typical engineering stress-strain curve obtained from a tensile test of HSLA steel at
room temperature, showing with various features
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6
stre
ss,
σ(M
Pa)
strain, ε (%)
Necking ZoneUniform elongation
Plastic zone
Elastic Zone
σUTS
σYS
0.2% offset
Fracture
E = 𝜎
𝜖
45
Figure 4.6 Typical true stress-strain curve obtained from a tensile test of an HSLA steel at room
temperature.
4.5.3 Charpy impact test property
Charpy test were conducted using a U-notched specimens. And impact energy and impact
toughness of an HSLA steel after calculatin found as:
Table 4.2 Charpy impact test property
Material Impact energy (J) Impact toughness 2
kJ
m
HSLA steel 67.52 1125.3115
0
100
200
300
400
500
600
700
800
900
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Tru
e st
ress
(M
pa
)
True strain (mm/mm)
True Stress vs. True strain
46
4.6 Elastic plastic fracture toughness (JIc and δIc)
Experimental J-integral and CTOD results of as-received steels as JIc and δIc are shown in figure
4.7 to 4.9, and figure 4.11 to 4.13 as a function of crack extension ∆a for displacement rates 0.03,
0.05 and 0.1mm/s using specimens of same thickness, results show from figure 4.10 and 4.14
that specimen ID: JIC-2 has maximum value of fracture toughness which is conducted at 0.03
mm/s displacement rate. The estimated J-integral fracture toughness values of the steel at room
temperature is decreases with increasing displacement rate all the results related resistance curve
and table shown below.
4.6.1 J- integral fracture toughness (JIc)
Figure. 4.7 Typical J-R curve of specimen ID: JIC-1 at room temperature.
0
100
200
300
400
500
600
0 0.5 1 1.5 2 2.5
J(k
J/m
2
Crack Extension (∆a) in mm
JQ=179.8 kJ/m2
∆alimit =1.85 mm
Specimen ID: JIC- 1
a/W = 0.45
W = 50.8 mm
bo = 27.94
Displacement rate =
0.05 mm/s
CONSTRUCTION
LINE
0.15 mm EXCLUSION LINE
0.2 mm OFFSET LINE
47
Figure 4.8 Typical J-R curve of specimen ID: JIC-2 at room temperature.
Figure 4.9 Typical J-R curve of specimen ID: JIC-3 at room temperature.
0
50
100
150
200
250
300
350
400
450
500
550
600
0 0.5 1 1.5 2 2.5 3
J (
kJ/m
2
Crack Extension (∆a) in mm
J-R curve
JQ = 228.2 kJ/m2
Specimen ID: JIC- 2
a/W = 0.581
Displacement rate =
0.03 mm/s
0
100
200
300
400
0 0.5 1 1.5 2 2.5 3 3.5 4
J(k
J/m
2
Crack Extension (∆a) in mm
J-R curve
JQ = 128.42 kJ/m2
Specimen ID- JIC-3
a/W = 0.542
Displacement rate =
0.1 mm/s
48
Table 4.3 Various JIc test parameter of investigate steel
Sample
ID a/W
bo
(mm)
σY
(MPa)
Displace
-ment
rate
(mm/s)
Jlimit
(kJ/m2)
Jmax
(kJ/m2)
∆alimit
(kJ/m2)
∆amin
(mm)
∆amax
(mm)
JQ
(kJ/m2)
JIC -1 0.45 27.94 700.536 0.05 2609.73 805.616 1.85 0.329 6.99 179.8
JIC -2 0.581 21.37 700.536 0.03 1996.061 837.14 1.82 0.336 5.34 228.2
JIC -3 0.542 23.37 700.536 0.1 2182.87 833.638 1.781 0.281 5.84 128.4
Table 4.4 Qualification criteria of JQ as JIc and evaluation of KJIc
Sample
ID
JQ
(kJ/m2)
bo
(mm)
B
(mm)
Thickness and
initial ligament
validity criteria
(mm)
0
10,
Q
Y
JB b
Fulfilled
The
validity
criteria?
Valid
value of
JIc
As JQ
(kJ/m2)
KJIc
(kJ/m2)
2
.
(1 )
IcE J
v
JIC -1 179.8 27.94 11.5 2.5666 Yes 179.8 205.845
JIC -2 228.2 21.37 11.95 3.2575 Yes 228.2 231.902
JIC -3 128.4 23.37 11.9 1.8329 Yes 128.4 173.952
Figure 4.10. JIc vs. displacement rate curve
100
150
200
250
0.02 0.04 0.06 0.08 0.1 0.12
JIc
(k
J/m
2)
Displcement rate in mm/s
49
4.6.2 CTOD fracture toughness (δIc)
Figure 4.11 Typical δ-R curve of specimen ID: JIC-1 at room temperature.
Figure. 4.12. Typical δ-R curve of specimen ID: JIC-2 at room temperature.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5
δ(m
m)
Crack Extension (∆a) in mm
δ-R curve
Specimen ID: JIC- 1
a/W = 0.45
W = 50.8 mm
bo = 27.94
Displacement rate =
0.05 mm/s
δQ = 0.0855 mm
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
δ(m
m)
Crack Extension (∆a) in mm
δ-R curve
δQ=0.151mm
Specimen ID:
JIC-2
a/W = 0.581
Displacement
rate = 0.03
mm/s
50
Figure 4.13. Typical δ-R curve of specimen ID: JIC-3 at room temperature.
Table 4.5 Various CTOD (δ) parameter of investigate steel
Sample
ID
a
W
bo
(mm)
Displacement
rate (mm/s)
δlimit
(mm)
δmax
(mm)
∆alimit
(mm)
∆amin
(mm)
∆amax
(mm)
δQ
(mm)
JIC -1 0.45 27.94 0.05 1.863 1.397 1.736 0.25 6.99 0.0855
JIC -2 0.581 21.37 0.03 1.425 1.0685 1.771 0.309 5.34 0.151
JIC -3 0.542 23.37 0.1 1.558 1.1685 1.629 0.281 5.84 0.073
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.5 1 1.5 2 2.5 3 3.5
δ(m
m)
Crack Extension (∆a) in mm
δ-R curve
δQ= 0.073 mm
Specimen ID: JIC-3
a/W = 0.542
Displacement rate = 0.1
mm/s
51
Table 4.6 Qualification criteria of δQ as δIc
Sample
ID
δQ
(kJ/m2)
bo
(mm)
initial ligament
validity criteria
0 10 Qb m
(mm)
Fulfilled
The validity
criteria?
Valid value of δIc
as δQ
(mm)
JIC -1 0.0855 27.94 1.71 Yes 0.0855
JIC -2 0.151 21.37 3.02 Yes 0.151
JIC -3 0.073 23.37 1.46 Yes 0.073
Figure 4.14 δIc vs. displacement rate curve.
0.06
0.09
0.12
0.15
0.025 0.055 0.085
δIc
(m
m)
Displcement rate in mm/s
52
Figure 4.15 Typical fracture surface and various region of CT specimen (JIC-1) after fracture.
4.7 Fractogrphy of JIc test fracture surface
The fracture specimen were observed by FESEM, a typical micrograph of the initial region of
the ductile crack extension is shown in figure 4.16 the fatigue pre-cracked region is found to be
followed by an expanse of stretch zone (SZ), which in turn is followed by ridges dimples of
ductile crack extension with all over microvoids are clearly visible.
A
.
53
Figure 4.16. FESEM micrographs of JIC-1 specimen are presented above as:
A). FESEM micrograph shows dimpled fracture surfaces that are typical of microvoid
coalescence.
B). High magnification of (A) showing the morphology of dimpled fracture surfaces and
microvoid coalescence.
C). High magnification factograph of the HSLA steel ductile fracture surface.
B
.
C
54
4.8 Constant amplitude loading interposed with mode-I overload and band overload
The curve drawn between crack length and number of cycle, from the data obtained from the
tests were normalization had done by the curve fitting procedure and the finally superimposed
curves are plotted alongside with the base line data in figure 4.17 of the steel and figure 4.18
shows the log-log plot of crack growth rates vs. stress intensity factors range curves for different
band overload. It is found that as the number of over load cycle increases amount of retardation
decreases and for 7 overload cycle the retardation is maximum.
Figure 4.17 Superimposed crack length vs. number of cycle curve.
0
5
10
15
20
25
30
35
40
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Cra
ck l
ength
, a
(mm
)
No. of cycle (N)
a (CL) mm
a (1ol)
a(3cycle ol)
a (5 ol)
a (10 ol)
a(ol 100)
a (7 cycle ol)
Crack growth retardation as 7>5>1>3>Const. load>100>10
55
Figure 4.18– Superimposed log da/dN versus log ∆K curve.
Figure 4.19 Various region of fracture surface of fatigue crack growth specimen imposed 7 cycle
overload
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
14lo
g d
a/d
N (
m/c
ycl
e)
log ∆K (MPa/√m )
da / dN (CAL) m/cyclesda / dN (10 cycle OL)da / dN (100 cycle OL)da / dN (1 cycle OL)da / dN (5 cycle OL)da / dN (3 cycle OL)da / dN (7 cycle OL)
Overload point
56
4.9 Fractogrphy of fatigue fracture surface
Few representative specimens were examined under Field emission scanning electron
microscope (FESEM). FESEM micrograph of constant amplitude loading test at R =0.3 are
shown in Figure 4.20 and fractographs of an HSLA steel tested at Rol = 1.25 are presented in
Figure 4.21. Although the surface indicates the presence of striations.
a.
57
Figure 4.20 FESEM micrographs of the constant amplitude load fatigue tested fracture surface
of an HSLA steel at stress ratio (R) = 0.3.
a.) A microscopic cracks and fine microscopic cracks with stable crack growth.
b.) In high magnification showing shallow striations in the region of stable crack growth.
b.
58
Figure 4.21 FESEM micrographs of the constant amplitude load imposed with 7 cycle tensile
overload fatigue tested fracture surface of steel at overload ratio (Rol) = 1.25.
1.) Overall morphology of fracture surface.
2.) In high magnification showing shallow striations absence of microvoides hinds insignificant
gross plastic deformation during overloading.
1.
2.
59
Chapter 5
ONCLUSIONS AND FUTURE WORK
5.1 Conclusions
In the present work, the elastic plastic fracture toughness test and fatigue crack growth study was
conducted on 1- CT specimen with reduced thickness of an HSLA steel.
The JIc tests were performed under three different displacement rate and finally the effect of
displacement rate on fracture toughness are studied.
In fatigue crack growth study three different loading conditions were applied: constant amplitude
loading with fixed stress ratios, constant loading interspersed with single spike overload, and
constant amplitude loading interspersed with multiple (band) spike overload. Effect of overload
and band overload on fatigue growth life are determined.
The conclusions drawn from the present work are summarized as follows:
1. The JQ fracture toughness values of 1-CT specimens with reduced thickness prepared
from the as received steel fulfills the validity criteria according to ASTM E-1820-13
standard. This JQ value can be used as fracture toughness value of this steel.
2. The experimental results of fracture toughness test show that the elastic plastic fracture
toughness parameters JIc and δIc decrease with increasing displacement rate.
3. The application of overload and band overload reduces the crack growth rate. However,
the extent of retardation is little (applied Rol =1.25).
4. Maximum retardation was observed on application of 7 overload cycles.
5. This enhanced retardation effect is explained on the basis of large plastic strain field zone
formed at the crack tip. The subsequent overload application may have resulted some
crack extension and reduced the effectiveness of plastic strain field region.
C
60
5.2 Suggested future work
(1) Fracture toughness test were carried out at three displacement rates only. However need
to be conducted over a wide range of displacement rates.
(2) The fracture toughness studies were done at room temperature. It is suggested to conduct
the test at low temperatures and elevated temperatures. Similar work may also be done
on the welded joints of an HSLA steel.
(3) Attempts may be made to use the model to predict fatigue life under overload and band
overload conditions.
(4) Fatigue crack growth studies may also be conducted applying realistic spectrum variable
amplitude conditions.
(5) Strain field distribution may be obtained using soft computing and CAE software under
various conditions
61
Chapter 6
EFERENCE
REFERENCES
[1] Brog TK, Jones JW, Was GS. Fatigue Crack Growth Retardation of INCONEL600.
Engineering Fracture Mechanics. 20 (1984); No. 2, pp. 313-320.
[2] Sander M, Richard HA. Finite element analysis of fatigue crack growth with interspersed
mode-I and mixed mode overloads. International Journal of Fatigue. 27 (2005); pp. 905-913.
[3] Sander M, Richard HA. Experimental and numerical investigations on the influence of the
loading direction on the fatigue crack growth. International Journal of Fatigue. 28 (2006); pp.
583-591.
[4] Anderson T L., Fracture Mechanics: Fundamentals and Applications. Boston CRC Press,
1995.
[5] Mohanty JR, Verma BB, Ray PK. Prediction of fatigue crack growth and residual life using
an exponential model: Part II (mode-I overload induced retardation) International Journal of
Fatigue. March 31 (2009); pages 425-432.
[6] Narasaiah N, Tarafder S, Sivaprasad S. Effect of crack depth on fracture toughness of
20MnMoNi55 pressure vessel steel. Materials Science and Engineering. A257 (2010); 2408-
2411.
[7]. Rice JR. A Path Independent J-Integral and the Approximate Analysis of Strain
Concentration by Notches and Cracks. Journal of Applied Mechanics June 35 (1968); pp. 379.
[8] Hertzberg, Richard W. Deformation and Fracture Mechanics of Engineering Materials (4 ed.)
1995; Wiley ISBN0-470-01214-9.
[9] Griffith AA. The Phenomena of Rupture and flow in solids. Philosophical Transitions of the
Royal Society of London. A221 (1921); pp. 163-169.
[10] Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. Journal
of Applied Mechanics. 24 (1957); pp. 361-364.
[11] Wells AA. Application of fracture mechanics at and beyond general yielding. Br Weld J.
10 (1963); pp. 563–570.
[12] Xian-Kui Zhu, James A. Joyce. Review of fracture toughness (G, K, J, CTOD, CTOA)
testing and standardization. Engineering Fracture Mechanics 85 (2012); pp. 1–46.
[13] Clarke GA, Andrews WR, Begley JA, Donald JK, Embley GT, Landes JD, et al. A
procedure for the determination of ductile fracture toughness values using J integral techniques.
J Test Evaluates. 7(1979); 49–56.
[14]. Standard Test Method for Plane-Strain Fracture Toughness of Metallic Material. Annual
Book of ASTM Standards, E1820-2013
R
62
[15] Barsom Jhon M, Rolfe Stanley T. Fracture and fatigue control in structures: Applications
of Fracture Mechanics, ASTM stock Number: MNL41, 1999.
[16] Kodama S., Misawa H, Hasegawa H, Nakayama H. The effect of strain rate on the J-
Integral. Engineering Fracture Mechanics (1978).
[17] Bannantine Julie A, Comer Jess J, Handrock James L. Fundamentals of Metal Fatigue
Analysis, Prentice Hall, Englewood Cliffs, New Jersy 1990.
[18] Ellyin F, Li HP. “Fatigue crack growth in large specimens with various stress ratios”.
Journal of Pressure Vessel Technology. 106 (1984); pp. 255–260.
[19] Gdoutos EE. Fracture Mechanics- An Introduction, Springer,2005.
[20] Broek, D, Elementary Engineering Fracture mechanics, Martinus Nijhoff Publishers, The
Hague,1982.
[21] Schijve J. Significance of Fatigue Cracks in Micro-Range and Macro-Range, Fatigue Crack
Propagation, ASTM STP 415, American Society for Testing and Materials, Philadelphia, 1967.
[22] McMillan JC, Pelloux RMN. "Fatigue Crack Propagation Under Program and Random
Loads," ASTM STP 415, American Society for Testing and Materials, Philadelphia, 1967.
[23] Von Euw E F J, Hertzberg RW, Roberts R, Delay Effects in Fatigue Crack Propagation.
ASTM STP 513, American Society for Testing and Materials, Philadelphia, 1973.
[24] Jones RE. Fatigue Crack Growth Retardation After Single-Cycle Peak Overload in Ti6A1-
4V Titanium Alloy. Engineering Fracture Mechanics 5 (1973).
[25] Wei RP, Shih TT. Delay in Fatigue Crack Growth. International Journal of Fracture, 10
(March 1974).
[26] Hardrath, HF McEvily AT. Engineering Aspects of Fatigue-Crack Propagation.
Proceedings of the Crack Propagation Symposium, Cranfield, England, 1 (October 1961).
[27] Schije J, Jacobs FA, Tromp, PJ, Crack Propagation in Clad 2024-T3A1 Under Flight
Simulation Loading. Effect of Truncating High Gust Loads. NNLR TR-69050-U, National
Lucht-En Ruimtevaart-Laboratorium (National Aerospace Laboratory NLR-The Netherlands),
June 1969.
[28] Hudson C M, and Hardrath H F. Effects of Changing Stress Amplitude on the Rate of
Fatigue-Crack Propagation of Two Aluminum Alloys, NASA Technical Note D-960, NASA,
Cleveland, September 1961.
[29] Von Euw EFJ. Effect of Single Peak Overloading on Fatigue Crack Propagation. Master's
dissertation, Lehigh University, Bethlehem, PA, 1968.
[30] Wheeler OE. Spectrum Loading and Crack Growth. General Dynamics Report FZM-5602,
Fort Worth, June 30, 1970.
[31] Willenborg J, Engle RM, and Wood HA, A Crack Growth Retardation Model Using an
Effective Stress Concept. Technical Memorandum 71-1-FBR, Air Force Flight Dynamics
Laboratory, January 1971.
[32] Elber W. The Significance of Crack Closure, Damage Tolerance in Aircraft Structures.
ASTM STP 486, American Society for Testing and Materials, Philadelphia, (1971), pp. 230-242.
63
[33] Wei RP, Shih TT. Delay in Fatigue Crack Growth. International Journal of Fracture. 10,
No. 1 (March 1974).
[34] Von Euw E F J, Hertzberg RW, Roberts R, Delay Effects in Fatigue Crack Propagation.
ASTM STP 513, American Society for Testing and Materials, Philadelphia, 1973.
[35] Gardner FH, Stephens RI. Subcritical Crack Growth Under Single and Multiple Periodic
Overloads in Cold-Rolled Steel. ASTM STP 559, American Society for Testing and Materials,
Philadelphia, 1974.
[36] Trebules Jr VW, Roberts R, Hertzberg RW, Effect of Multiple Overloads on Fatigue Crack
Propagation in 2024-T3 Aluminum Alloy. ASTM STP 536, American Society for Testing and
Materials, Philadelphia, 1973.
[37] Standard Test Methods for Tension Testing of Metallic Materials. Annual Book of ASTM
Standards, E8/E8M-13a, 2013.
[38] Indian Standard METHOD FOR CHARPY IMPACT TEST (U-NOTCH) FOR METAL
UDC 620.178.746.22:669, IS: 1499 – 1977, Reaffirmed 2003.
[39] Standard Test Method for Measurement of Fatigue Crack Growth Rates, Annual Book of
ASTM Standards, E647, 2013.
